The proposed methods enable us to study a model of stochastic evolution that includes Markov switchings and to identify the
diffusion component and big jumps of perturbing process in the limiting equation. Big jumps of this type may describe rare
catastrophic events in different applied problems. We consider the case where the perturbation of the system is determined
by an impulse process in the nonclassical approximation scheme. Special attention is given to the asymptotic behavior of
the generator of the analyzed evolutionary system.

Asymptotic analysis of the large deviation problem for impulsive processes in the scheme of Poisson approximation is
performed. Large deviations for impulsive processes in the scheme of Poisson approximation are defined by an exponential
generator for a jump process with independent increments.

We investigate an impulsive storage process switched by a jump process. The switching process is, in turn, averaged. We prove the weak convergence of the storage process in the scheme of series where a small parameter ε tends to zero.

We determine the regular and singular components of the asymptotic expansion of a semi-Markov random evolution and show the regularity of boundary conditions. In addition, we propose an algorithm for finding initial conditions for t = 0 in explicit form using the boundary conditions for the singular component of the expansion.